Learning Objective:
What does Kurtosis relate to?
How to measure Kurtosis?
Concept:
Kurtosis relates to bulginess, peakedness, tailedness of a frequency distribution.
Leptokurtic frequency distribution is narrow with sharp peak and extended tails.
Mesokurtic frequency distribution is normal with less sharp peak and not much extended tails.
Platykurtic frequency distribution is like platypus without sharp peak and very less extended tails.
Kurtosis is measured with Pearsonian's Coefficient of Kurtosis which is based on central moments.
If γ₂ > 0, the frequency distribution is Leptokutic.
If γ₂ = 0, the frequency distribution is Mesokurtic.
If γ₂ < 0, the frequency distribution is Platukurtic.
Formulas:
Pearsonian's Coefficient of Kurtosis
β₂ = μ₄ / μ₂²
γ₂ = (β₂ - 3)
Pearson kurtosis does not measure sharpness or flatness at all. You can have very low Pearson kurtosis for an infinitely peaked distribution, and you can have a very high Pearson kurtosis for a perfectly flat-topped distribution. Pearson kurtosis only measures tail weight.